Gompf, Robert E. An exotic menagerie. (English) Zbl 0808.57012 J. Differ. Geom. 37, No. 1, 199-223 (1993). In a quest to further demonstrate the perversities that occur in dimension four, the author describes further interesting constructions of uncountably many exotic smooth structures on \(\mathbb{R}^ 4\) and other open 4-manifolds. In particular, the author shows that for any topological 4- manifold \(M\), \(M\)-pt. admits uncountably many smoothings. He then goes on to explicitly construct exotic smooth structures on \(\mathbb{R}^ 4\). Finally, he deftly compares and relates the various constructions of these exotic \(\mathbb{R}^ 4\). Reviewer: R.Stern (Salt Lake City) Cited in 1 ReviewCited in 11 Documents MSC: 57N13 Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010) 57R55 Differentiable structures in differential topology 57R57 Applications of global analysis to structures on manifolds Keywords:smooth structures on punctured 4-manifolds; uncountably many exotic smooth structures on \(\mathbb{R}^ 4\); open 4-manifolds PDFBibTeX XMLCite \textit{R. E. Gompf}, J. Differ. Geom. 37, No. 1, 199--223 (1993; Zbl 0808.57012) Full Text: DOI